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lfunc_lfunctions • Show schema
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{'Lhash': '2127225168345627200861426005444', 'a10': [-22.98213966788372, -3.464000197844659], 'a2': [-0.7689680574070051, -0.23719523254007543], 'a3': [-8.727627389407328, 22.237631918937392], 'a4': [-25.904590483139273, -17.661450743650814], 'a5': [28.559193680245254, -4.304605836892612], 'a6': [11.985926953557682, -15.029877009883695], 'a7': [-107.94659139134652, 71.79507926724278], 'a8': [31.78609128395148, 39.85849775940133], 'a9': [-240.20918865916232, -222.8815555442198], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.8588071708360525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [107.94659139134652, -71.79507926724278]]]], 'bad_primes': [7], 'central_character': '49.2', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '309182529915493184957356020173', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7689680574070051, 0.23719523254007543], [26.439640778111837, 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'-0.05499465482289092 + 0.9984866488546109*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.258757089121', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67808477191005070143749659636', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.23080505994607459204424958433', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.46580606349733893252682319291', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.8588071708360525, 'bad_primes': [7], 'central_character': '49.2', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/6/g/a/2/12'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-7e2-49.2-c5-0-14', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.2-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8033564116672807, 'root_angle': 0.2587570891214907, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67808477191005070143749659636', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2127225168345627200861426005444', 'Lhash_array': ['2127225168345627200861426005444'], 'label': '2-7e2-49.2-c5-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/6/g/a/2/12'}